Exact non-Hermitian mobility edges in one-dimensional quasicrystal lattice with exponentially decaying hopping and its dual lattice

We analytically determine the non-Hermitian mobility edges of a one-dimensional quasiperiodic lattice model with exponentially decaying, hopping, and complex potentials as well as its dual model, which is just a non-Hermitian generalization of the Ganeshan-Pixley--Das Sarma model with nonreciprocal nearest-neighboring hopping. The presence of the non-Hermitian term destroys the self-duality symmetry and, thus, prevents us exploring the localization-delocalization point through looking for self-dual points. Nevertheless, by applying Avila's global theory, the Lyapunov exponent of the Ganeshan-Pixley--Das Sarma model can be exactly derived, which enables us to get an analytical expression of mobility edge of the non-Hermitian dual model. Consequently, the mobility edge of the original model is obtained by using the dual transformation, which creates exact mappings between the spectra and the wave functions of these two models.